A Linear Model of Wintertime Low-Frequency Variability. Part I: Formulation and Forecast Skill

A linear inverse model (LIM) suitable for studies of atmospheric extratropical variability on longer than weekly timescales is constructed using observations of the past 30 years. Notably, it includes tropical diabatic heating as an evolving model variable rather than as a forcing, and also includes, in effect, the feedback of the extratropical weather systems on the more slowly varying circulation. Both of these features are shown to be important contributors to the model's realism. Forecast skill is an important test of any model's usefulness as a diagnostic tool. The LIM is better at forecasting week 2 anomalies than a dynamical model based on the linearized baroclinic equations of motion (with many more than the LIM's 37 degrees of freedom) that is forced with observed (as opposed to the LIM's predicted) tropical heating throughout the forecast. Indeed, at week 2 the LIM's skill is competitive with that of the global nonlinear medium-range forecast (MRF) model with nominally O(106) degrees of freedom in use at the National Centers for Environmental Prediction (NCEP). Importantly, this encouraging model performance is not limited to years of El Niño or La Niña episodes. This suggests that accurate prediction of tropical diabatic heating, rather than of tropical sea surface temperatures per se, is key to enhancing extratropical predictability. The LIM assumes that the dynamics of extratropical low-frequency variability are linear, stable, and stochastically forced. The approximate validity of these assumptions is demonstrated through several tests. A potentially limiting aspect of such a stable linear model with decaying eigenmodes concerns its ability to predict anomaly growth. It is nevertheless found, through a singular vector analysis of the model's propagator, that predictable anomaly growth can and does occur in this dynamical system through constructive modal interference. Examination of the dominant growing singular vectors further confirms the importance of tropical heating anomalies associated with El Niño/La Niña as well as Madden–Julian oscillation episodes in the predictable dynamics of the extratropical circulation. The relative contribution of initial streamfunction and heating perturbations to the development of amplifying anomalies is similarly examined. This analysis suggests that without inclusion of the effects of tropical heating, extratropical weekly averages may be predictable about two weeks ahead, but with tropical heating included, they may be predictable as far as seven weeks ahead.